Optimization of an Adsorbed Natural Gas System …...Optimization of an Adsorbed Natural Gas System with Phase Change Material using the Topology Optimization Method Diego Silva Prado

Optimization of an Adsorbed Natural Gas System with Phase ChangeMaterial using the Topology Optimization Method

Diego Silva Prado

Emilio Carlos Nelli Silva

Ricardo Cesare Roman Amigo

[email protected]

[email protected]

[email protected]

Dept. of Mechatronics Engineering and Mechanical Systems of the University of Sao Paulo

Abstract. Natural Gas has been drawing industrial sectors attention as a promising alterna-tive fuel. This solutions attractiveness depends on the quality and efficiency of the storage andtransport methods employed. Porous media are known to be an efficient manner to store naturalgas by the adsorption mechanism, also known as Adsorbed Natural Gas (ANG). Temperatureexerts significant influence on adsorption efficiency. Studies applying Phase Change Materials(PCM) as heat exchanger in ANG systems suggests the combination improves the vessel ca-pacity and adsorption and desorption rates behavior. In addition, the PCM bodies shape andposition inside adsorption systems greatly affects the benefits they bring. For this reason, theTopology Optimization Method (TOM) is indicated for this problem. The topology optimizationmethod is a versatile tool for material distribution inside a domain and in the last few decadesits capabilities of exploring manufacturing process characteristics as well as its implementa-tion have been improved. This study aims to increase the capacity and performance of AdsorbedNatural Gas (ANG) Vessels using TOM to distribute PCM material in the vessel interior. Thephysical model consider a coupled heat and mass transfer trough an ANG vessel with PCM inits interior, the boundary conditions are dictated by a pressure input in the vessels extremityand the natural convection on the vessels walls. FEniCS Project libraries are employed in thegoverning equations implementation and to work the solution for the differential equations anddolphin-adjoint libraries are applied to perform the sensitivities calculus. The project variable

CILAMCE 2016Proceedings of the XXXVII Iberian Latin-American Congress on Computational Methods in Engineering

Suzana Moreira Avila (Editor), ABMEC, Braslia, DF, Brazil, November 6-9, 2016

Optimization of an ANG System with PCM using the Topology Optimization Method

for the optimization is defined as the PCM distribution inside the vessel. Thermal propertiescorrections are performed according to an analytical solution for the phase change problem.Phase change enthalpy corrections are performed in the level of the variational problem tomodel the phase change phenomena. The amount of heat transferred to the phase change en-thalpy dictates the phase composition in the domain. The implementation benefits the topologyoptimization approach as it maintains the duality between the adsorbent volume to adsorb gasand the PCM volume to store heat. An experimental work from the literature is modelled andcompared to the numerical results for software validation and model properties calibration. Asresults a 2D ANG vessel optimization is performed, the final topologies are presented and theirtotal adsorption volume and charging/discharging time are compared.

Keywords: Adsorption, Optimization, PCM, ANG, Desorption

CILAMCE 2016Proceedings of the XXXVII Iberian Latin-American Congress on Computational Methods in EngineeringSuzana Moreira Avila (Editor), ABMEC, Braslia, DF, Brazil, November 6-9, 2016

D.S. Prado, E.C.N. Silva

1 INTRODUCTION

Adsorption consists in the adhesion of molecules to surfaces, attracted by disrupted bonds.The modelling of the adsorption phenomena can be found in the literature such as in (Freniet al., 2009; Sahoo et al., 2014). The Adsorbed Natural Gas (ANG) technology employs theadsorption phenomena to store and transport gas in a porous solid matrix. This method ofstorage offers a similar volume capacity (164 V/V) to the Compressed Natural Gas (CNG) wichcan provide 245 V/V. However ANG operates in pressures one magnitude order lower thanCNG, being a safer option.

In the last few decades the Phase Change Materials (PCM) drawn scientific community’sattention for its ability to increase the capacity of thermal storage systems for various applica-tions (Padovan et al., 2014).

Phase change materials are substances which have a high phase change hentalphy and,therefore, are considered latent thermal storage materials (Sharma et al.,2009). Taking an ex-ample of a solid-liquid PCM material outside its phase change temperature, it behaves as aconventional material storing heat as it is heated and elevating its temperature, but when thephase change occurs, large amount of heat is stored due to the change of state of the material.Different from materials used for sensible heat storage systems, PCM absorbs and releases largeamounts of heat at practically constant temperature during its phase change, for the same vol-ume, a PCM stores 5 to 14 times more heat than water (Sharma et al.,2009). Yet, such materialsgenerally have high thermal conductivity, allowing for high charge rates and discharge thermalenergy.

There is a huge range of PCMs and to better organize them, they were conventionallygrouped in organic, inorganic and eutectic (Sharma et al.,2009). The material proposed here,HS34, belongs to the group of inorganic, with a salt hydrate. This type of MMF is the moststudied group and most used in latent heat storage systems (Sharma et al.,2009). The solid-liquid transformations of salt hydrates are, in fact, hydration and dehydration processes. Thus,a salt hydrate, in general, melt to a state with less moles of water in their chemical compositionor their anhydrous form (without the presence of water). The phase change hentalphy of thesubstance is the energy needed to make this break in its structure. The most attractive attributesof salt hydrates are its high heat of fusion per unit volume, relatively high thermal conductiv-ity (almost double the paraffin) and minimum variations in the volume during phase change(Sharma et al.,2009). For correct selection of an MMF material for a given application, the op-erating temperature of both the heating and the cooling must match the transition temperatureof the material MMF (Sharma et al.,2009).

In (Toledo et al., 2013) the behavior of a carbon dioxide adsorbent tank (CO2) aided by aset of fixed PCM balls in its interior was studied. The study carried out computer simulationsand the results obtained were confronted with an experimental test. The experiment shows thatthe maximum temperature inside the tank with the MMF spheres is lower than that measured onthe tank with PCM. Also, for different pressures of adsorption, the storage capacity of the tankwith PCM was higher than that for the tank with no PCM. Furthermore, the study of (Toledoet al., 2013) shows the existing influence between the volume of the spheres and the effect theyhave on the system performance. In (Li et al., 2015), an methane adsorption vessel employingpetroleum coke as adsorbent and a mixture of lauric acid and dodecanoic acid as phase changematerial is studied. An experimental vessel is built and the adsorption cycle and desorption




cycle are performed aiming to compare an ANG vessel with PCM and an ANG vessel withoutPCM. (Li et al., 2015) verifies an increase of adsorbed and desorbed gas in the vessel withPCM. Hence both studies, (Toledo et al., 2013; Li et al., 2015), indicate PCM as an effectivealternative for a passive thermal control in an adsorption tank.

In this work, the topology optimization method is employed to performer a material dis-tribution inside an adsorption vessel in order to extremize the amount of adsorbed gas. Once(Toledo et al., 2013) stated that the geometry and position of PCM bodies affect the behaviourof the tank, TOM is a promising method to handle the proposed problem.

2 Physical Problem Formulation

In this study, the fluid velocity is given by the pressure gradient as stated by the Darcy Law.The local thermal equilibrium is considered so that for a certain region on the domain, a singletemperature value can determine the temperate for the gas and for the solid (their temperature isthe same). The methane thermal capacity is considered constant for all the temperature range inthe analysis. All PCM properties are considered isotropic, the adsorption enthalpy is assumedto be invariable throughout the whole process. Finally, the equilibrium pressure is given as afunction of temperature (Chung et al., 2009):

Peq(T ) = Pref · e(A−B

T

)(1)

where A and B are constants and Pref is the reference pressure.

For the adsorption physical problem it is necessary to express the mass and energy balancein terms of temperature and pressure as described in (Freni et al., 2009):

ε∂

∂t

(P

T

)−∇ ·

(Ks

µg· PT· ∇P

)= −(1− ε)∂ρs

∂t

Ks

µg(2)

εCpsMgP

RgT

∂T

∂t− Mg

Rg

∇ ·(CpgKs

µg· ∇P · P

)+ (1− ε)ρsCps

∂T

∂t

−∇ · (ks · ∇T ) = (1− ε)|∇H|∂ρs∂t

+Hpcm

(3)

where ε is the porosity, µg is the fluid viscosity,Rg is the ideal gas constant, Mg is the molecularmass of the gas, Ks is the medium permeability, Cps is the solid phase specific heat, Cpg is thegas phase specific heat, ks is the medium thermal conductivity and Hpcm is the heat absorbed orreleased due the the phase change process.

The adsorbent bed density variation in adsorption and in desorption is determined by finitedifferences as follows (Mayer et al., 1987):

∂ρs∂t

= Ga(ρss − ρs) (4)

where ρss is the saturation density for the adsorbent bed and Ga is given by:

Ga = Da exp

(−EaRgT

)ln

(P

Peq

)(5)



where Da is the kinetic constant for adsorption, Ea is the adsorption activation energy and Peqis the equilibrium pressure. For the dessorption phase:

∂ρs∂t

= Gd(ρs − ρs0) (6)

where ρs0 is the initial density (density of the adsorbent with no gas) and Gd is given by:

Gd = Dd exp

(−EdRgT

)(P − PeqPeq

)(7)

where Dd is the kinetic constant for dessorption, Ed is the dessorption activation energy.

For the adsorption equilibrium state the following relation can be written (Sahoo et al.,2010):

qss = ρs0 + ρadsWs exp

(−(A

Ea

)ns)

(8)

where ρads is the adsorbed gas density, Ws is the specific pore volume, ns is the affinity coeffi-cient and A is the Polanyi adsorption potential given by:

A = RgT ln

(PsatP

)(9)

where Psat is given by:

Psat = Pcr

(T

Tcr

)2

(10)

where Pcr is the critical pressure and Tcr is the critical temperature of the gas.

3 Phase Change Material Model

The phase change material formulation follows the one dimensional analytical model fromthe Stevan Phase Change Problem. The phase change barrier position is given by:

δ(tmel) = 2 · β ·√αl · tmel (11)

where αl is the thermal difusivity of the liquid phase, tmel is the amount of time that the solidphase spent melting, β is given as the solution for the non-linear equation:

βeβ2

erf(β) =Cp,l(Tw − Tm)

L√π

(12)

where Cp,l is the specific heat of the liquid phase, Tm is the phase change temperature and Twis the node temperature. The heat stored in the phase change phenomena can be directly relatedto the phase change barrier. Hence the heat consumed or released by the PCM body is writtenas:

Hpcm = εpcm · ρpcm · L ·∂δ(tmel)

∂t(13)

This approach aims to apply the 1D analytical model in the element nodes in order torepresent the PCM phase change enthalpy inside the studied domain.




4 Finite Element Formulation

The weak forms of the equations from section 2 and section 3 are discretized over a 3-nodeelement with order 1 for temperature and order 2 for pressure and density. In order to solve theadsorption physical problem the following non-linear system is solved via the finite elementsmethod. W(T) Z(P,T)

0 N + Lc(T ) + Lr(P, T )

P

T

+

Qc(T ) +Qr(P, T ) 0

Jc + Jr(P ) K + Dr

P

T

=

G

H + Dc

(14)

where the matrices coefficients are the result of the approximation of the governing equationson a finite element inside the domain.

5 Topology Optimization Method for Adsorption Systems

The TOM has been employed to design optimized adsorption vessels with PCM by dis-tributing the PCM material inside the domain. In this work TOM aims to extremize an ob-jective function for a vessel exposed to a transient pressure input and natural convection. Theoptimization problem is stated bellow:

Maximize : Ja =∫

Ωsρs(Tf )dx

s.t. : 0 ≤ εpcm ≤ 1

(15)

where Tf is the final time for the transient analysis.

5.1 Material Model for Topology Optimization

In this work, it is assumed that the elements represent regions in the domain space. The εpcmis the project variable which defines the portion of PCM inside an element inside the domain,it can vary from 0, no PCM, to 1, 100% of PCM. Hence an element is a mixture of PCM andadsorbent and gray scales (intermediate values between 0 and 1) are allowed. For the propertiesrelated to the PCM portion inside an element, the material model is as follows:

For the barrier position ans, thus, the amount of heat in the phase change, it can be writtenas:

δ(εpcm) = 2 · εpcm · β ·√αl · tmel (16)

The specific heat can be stated as:

Cp(εpcm) = Cppcm · εpcm + Cpads · (1− εpcm) (17)



The thermal conductivity can be stated as:

k(εpcm) = kpcm · εpcm + kads · (1− εpcm) (18)

The initial density can be stated as:

ρs0(εpcm) = ρpcm · εpcm + ρs0ads · (1− εpcm) (19)

The saturation density can be stated as:

ρss(εpcm) = ρpcm · εpcm + ρssads · (1− εpcm) (20)

6 Results

Given the initial domain, exhibited in fig 1b. A 3200 element mesh with a initial PCMdistribution is studied. A topology optimization analysis is run assuming this initial conditionsand a transient pressure input in the left corner of the domain. The heat is assumed to leavethe domain only by natural convection and the right corner of the domain is considered to beinsulated. The boundary conditions are presented in fig 2.

Figure 1: a) The mesh employed in the analysis. A 3200 mesh composed by triangular elements. b) Theinitial domain for the topology optimization. The gray region is 100% adsorbent and the green region is thePCM region

For the analysis, the properties values were assumed as for Maxsorb III and methane foradsorption and lauric acid for PCM. Assuming Patm = 101350.0Pa, Tatm = 293.0K, hroom =16.0 W

m2·K , Ea = 10626.0 kgm3 , Rg = 8.31 J

molK, Rs0 = 318.00 kg

m3 , Rag = 422.36 kgm3 , Wf =

1.01 · 10−3 kgm3 , Pcr = 4.6MPa, Tcr = 190.0K and np = 2.0.

Figure 2: Boundary Conditions for topology optimization. The pressure profile as a function of time andthe natural convection in the upper and lower boundaries o the vessel.




Figure 3: a) The objective function values throughout the iterations. b) The material distribution inside thedomain. The blue regions have less PCM in the composition and the red regions have higher amounts ofPCm in the composition.

The optimization run results are show in fig 3. In fig 3a, the objective function behaviour isshown. After 10 iterations it becomes stable and in fig 3b, the material distribution for the 15th

iteration is presented as the optimized result.

The topology optimization method is able to distribute the PCM material inside the studieddomain. The optimized solution contains 7.9 liters more gas than the initial design consideringthe same time for the adsorption cycle.

The PCM distribution is highly affected by the conductivity of the materials in the domain.It can be seen in fig 3b that the copper tube in the center of the domain impacts in the materialdistribution, showing that PCM is mostly placed in regions with lower conductivity. However,in the right extremity of the tube, a PCM composition can be verified. This suggests that highconductivity doesn’t nullifies the benefits of PCM in adsorption vessels and they must be placedand quantified in a manner to operate with synergy inside the system.

ACKNOWLEDGEMENTSThe author acknowledges CAPES and FUSP for providing him with a doctoral schol-

arship. We acknowledge the support of the RCGI Research Centre for Gas Innovation,sponsored by FAPESP (2014/50279-4) and BG Group Brasil.

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Freni, A., Cipit, F., Cacciola, G., 2009. Finite element-based simulation of a metal hydride-based hydrogen storage tank. International Journal of Hydrogen Energy, 34, 85748582. doi:10.1016/j.ijhydene.2009.07.118

Li, X., Li, Y., 2015. Applications of organic phase change materials embedded in adsorbents forcontrolling heat produced by charging and discharging natural gas. Adsorption, 21(5), 383389.doi:10.1007/s10450-015-9678-4

Mayer, U., Groll, M., Supper, W. (1987). Heat and mass transfer in metal hydride reactionbeds: Experimental and theoretical results. Journal of the Less Common Metals, 131, 235244.doi:10.1016/0022-5088(87)90523-6



Padovan, R., Manzan, M., 2014. Genetic optimization of a PCM enhanced storage tank for So-lar Domestic Hot Water Systems. Solar Energy, 103, 563573. doi:10.1016/j.solener.2013.12.034

Sahoo, P., Ayappa, K., John, M. (2010). Simulation of Methane Adsorption in ANG StorageSystem. Proceedings of the COMSOL Conference 2010 India, 27. Retrieved from http://www.comsol.no/paper/download/101175/sahoopaper.pdf

Sahoo, P. K., Prajwal, B. P., Dasetty, S. K., John, M., Newalkar, B. L., Choudary, N. V.,Ayappa, K. G., 2014. Influence of exhaust gas heating and L/D ratios on the discharge ef-ficiencies for an activated carbon natural gas storage system. Applied Energy, 119, 190203.doi:10.1016/j.apenergy.2013.12.057

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Optimization of an Adsorbed Natural Gas System …...Optimization of an Adsorbed Natural Gas System with Phase Change Material using the Topology Optimization Method Diego Silva Prado